geometry, circumference?

Question

I'm troubled with a question in which I have to obtain the equation of a circumference that contains the points E(4,5), F(3,-2) y G(1,-4). Any idea?

I don't think that finding the center of the triangle EFG and calculating its center will help, because the points are not distributed uniformly aroud the circumference

I don't think that finding the center of the triangle EFG and calculating the distance between any of the points and the center as a radius will help, because the points are not distributed uniformly aroud the circumference

Answer 1

The general equation of the circle is (x-a)² + (y-b)² = c². Notice that there are 3 unknowns, a, b, c, and we have 3 points (4,5), (3,-2), (1,-4), thus setting up the necessary 3 equations for a determinate solution. The unique answer where c, the radius, is positive is:

a = -7/2
b = 5/2
c = 5√(5/2)

The longer way to solve this is to find the equations of the lines perpendicular to and going through the midpoints of at least 2 of the line segments connecting the 3 given points, and then finding the point of intersection, which would be the center of the circle. Etc., etc. I like the other way better.

Answer 2

Draw a triangle with those coordinates.
Find the center point.
Find the Radius r

c=pi r squared